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措尔曲面.
数学上,措尔曲面(英语:Zoll surface)是一种有类似球面的性质的曲面。若一个曲面同胚于2-球面,并有黎曼度量,使得所有测地线都是闭合及等长的,就称为措尔曲面。2-球面上的单位球面度量显然有此性质,且有无穷维族几何相异的形变,也都是措尔曲面。特别是措尔曲面大多数都没有常曲率。
措尔曲面以奥托·措尔(Otto Zoll)命名。他是希尔伯特的学生,最先发现措尔曲面的非平凡例子。
参考
- Besse, A.: "Manifolds all of whose geodesics are closed", Ergebisse Grenzgeb. Math., no. 93, Springer, Berlin, 1978.
- Funk, P.: "Über Flächen mit lauter geschlossenen geodätischen Linien". Mathematische Annalen 74 (1913), 278–300.
- Guillemin, V.: "The Radon transform on Zoll surfaces". Advances in Mathematics 22 (1976), 85–119.
- LeBrun, C.; Mason, L.: "Zoll manifolds and complex surfaces". Journal of Differential Geometry 61 (2002), no. 3, 453–535.
- Zoll, Otto; Ueber Flächen mit Scharen geschlossener geodätischer Linien. (German) Math. Ann. 57 (1903), no. 1, 108–133.
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